I have a lot of midterms and papers due the week before and the monday/tuesday immediately preceding the October LSAT.

One professor agreed to change the midterm date because so many people complained about the LSAT timing (it was a political science class, big surprise).

I haven't asked any of my professors yet but I wonder if any of them will allow me to hand in papers/tests a bit later. The only professors I would ask this out of are professors I've already taken classes with before (and done well, got A's).

Good idea? Or bad impression? I'm definitely going to ask one of these professors for a LOR so I'm afraid it might make me look bad?

Well, it could show your dedication to the legal profession (that you actually are concerned about your performance on the LSAT).

What if you just ask the professors you're not planning on getting LORs from? That way, you might get most of them extended, and still have that one professor's assignments - but probably manageable now that you've pushed the other stuff forwards.

I got lucky and ended up with only 2 tests on the Monday in the week before the LSAT. The week after is disgusting, but I'll deal with that then.